The move comes as city chiefs face an expected 39 million target in efficiency savings over three years as a result of a tighter Westminster settlement for Scotland.

The first steps down the privatisation road will be taken in the next few weeks when council chiefs invite firms to submit ideas to improve the customer-facing areas of the council, such as council tax collection or its call centre.

This initiative will see companies come in and manage or reorganise council departments, with them splitting the money saved with city leaders. However, other methods of reorganising services, such as setting up arms-length operating trusts like Edinburgh Leisure, are also under consideration.

It is hoped a list of services which could be transferred out of direct council control will be drawn up by the summer.

Councillor Mackenzie said: "There is no question that the council is likely to face unprecedented pressure on its finances over the coming years.

"We know, frankly, that in some areas we are not doing the best job we can and efficiencies can be made, but it is a case of identifying what is right for Edinburgh."

Councillor Mackenzie said it was the intention that any new business units created would look to bid for new work from private companies in the long-term.

Unison's service conditions convener John Ross said he had immediate concerns.

"We are very resistant to external organisations making profit out of public services. That profit should be reinvested into the services provided and not pocketed by some private company.

"We are meeting with the chief executive in a couple of weeks but we are against his concept from the outset – it doesn't stack up.

"Our members provide a good service across a range of areas and you have to question if this will continue if they are trying to make major financial savings."

City leaders have flirted with the idea of wholesale privatisation of its services in recent years.

The most high-profile example was hiring management consultancy firm Pinnacle at a cost of 3.6m to carry out a shake-up of the council's waste department.

The firm brought in changes designed to save 11.7m over the next three years.

Councillor Andrew Burns, the city's Labour leader, said: "It is absolutely essential that this is done in an open and transparent basis and the fact that this has not been near a council committee for proper scrutiny is not on. There is a real danger of a reduction in the level of service provided to the people of Edinburgh."

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